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«SYRTO WORKING PAPER SERIES Working paper n. 14 | 2015 This project has received funding from the European Union’s Seventh Framework Programme for ...»

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Insights to the European debt crisis

using recurrence quantification

and network analysis

Peter Martey Addo

SYRTO WORKING PAPER SERIES

Working paper n. 14 | 2015

This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and

demonstration under grant agreement n° 320270.

This documents reflects only the author's view. The European Union is not liable for any use that may be made of the information contained therein.

Insights to the European debt crisis using recurrence quantification and network analysis Peter Martey ADDOa,b,∗ a Centre National de la Recherche Scientifique (CNRS), France ´ b Centre d’Economie de la Sorbonne (CES) - CNRS : UMR8174 - Universit´ Paris I - e Panth´on Sorbonne, France e Abstract The turmoil in the sovereign debt markets in Europe has raised concerns on the usefulness of sovereign credit default swaps and government bond yields in periods of distress. In addressing this issue, we introduce a novel nonlinear approach for the analysis of non-stationary multivariate data based on complex networks and recurrence analysis. We show the relevance of the approach in studying joint risk connections, extracting hidden spatial information, time dependence, detection of regime changes and providing early warning indicators. The feasibility and relevance of the approach in studying systemic risk is discussed. Finally, we share more light on possible extensions and applications of the approach to systemic risk.

Keywords: Sovereign debt crisis, Economic growth, Financial stability, Systemic risk JEL: C40, E50, G01, G18, G21 ´ ∗ Correspondence to: Centre d’Economie de la Sorbonne (CES) - CNRS : UMR8174

- Universit´ Paris I - Panth´on Sorbonne, 106-113 boulevard de l’hopital, 75013, Paris, e e France.

Email address: peter.addo@univ-paris1.fr (Peter Martey ADDO) URL: http://pkaddo2000.weebly.com/ (Peter Martey ADDO) Preprint submitted to Elsevier May 12, 2015

1. Introduction The recent turmoil in the sovereign debt markets in the European Mone- tary Union has drawn much attention to vulnerabilities of the banking system and the whole financial system in periods of distress. Some of the recent no- table works documented in literature include Billio et al. (2012); Bisias et al.

(2012); Acharya et al. (2013); IMF (2013); Chan-Lau et al. (2015) and the ref- erences therein. Despite ongoing economic recovery, much work still need to be done to address sovereign risks and strengthen confidence in the financial system. In this respect, our study is aimed at contributing to the prevention of crisis by highlighting policies and indicators that may mitigate systemic risks to enhance financial stability. This study seeks to play a role in examining the usefulness in terms of financial stability implications of government bonds and sovereign credit default swaps (SCDS) prior to and during the European debt crisis. A key concern has been whether SCDS prices provide indications of sovereign credit risk in the same fashion as the underlying government bond yields. It is unclear as to which of these market indicators react more rapidly to new information during periods on distress. To this date, there is still heated debate on the impact of SCDS on the stability of financial markets especially in periods of stress. In addressing issues on the usefulness of these market indicators, this paper seeks to provide evidence to assess the possible impact of some European Central Bank (ECB) policies on financial stability. In particular, this paper comments on ECB’s bond purchasing programmes and the European Union (EU) ban on purchases of naked sovereign CDS on November 1, 2012, during the debt crisis.

2 To address this issue, we make use of recurrence quantification analysis (RQA) (Zbilut and Webber (1992); Marwan and Kurths (2002)) and recurrence networks (Marwan et al. (2009); Donner et al. (2010)) to study the dynamics of the sovereign debt crisis across time. The RQA and recurrence networks are quantitative extensions of recurrence plots (Eckmann et al.

(1987); Marwan et al. (2007); Addo et al. (2013)). These extensions are useful in examining dynamical transitions and regime change detection, the detection of phase synchronization, or the quantitative characterization of the dynamics of underlying time series data (see Marwan et al. (2007); Donner et al. (2011); Donges et al. (2012)). It is worth pointing out that recurrence network do not directly require knowledge about the time arrangement of observations as required by “correlation” methods such as (linear or nonlinear) autoregressive models, and mutual information models. Recurrence networks relies on the spatial structure of time series in phase space, and thus in investigating spatial dependences in the underlying process. In this paper, we provide network statistics based on recurrence networks suited for identifying dynamical transitions, which can serve as systemic risk indicators or early warning measures. Aside the ability of the method to trace dynamical transitions (Donges et al. (2011)), it is applicable to non-stationary time series data. Recurrence networks allow for an intuitive and natural interpretation of results. Unlike some econometric models, recurrence networks analysis does not require stationarity or any pre-processing of the original data (Marwan et al. (2009); Donner et al. (2010)). Hence, pre-processing of the data before recurrence network analysis will depend on the researcher’s interest or the particular real-world problem considered. To our best of knowledge, 3 this paper will serve as the first application of recurrence networks in finance and economics discipline.





This study finds some evidence that the European Monetary Union (EMU) is still in sovereign debt crisis although the government bond yields indicates signs of possible recovery in terms of reduced interest rates on government debts. Our findings suggest that the SCDS market are as useful as the government bond market in reflecting economic fundamentals and can be a useful mechanism to hedge sovereign credit risks to enhance financial stability in EMU economies. Overall, even though there is evidence of structural changes or transitions in both SCDS and government bond yields during periods of distress, it is more pronounced in sovereign CDS market. Sovereign CDS prices appear to react faster to new information via transitions than sovereign bond yields during periods of distress.

Overall, the study finds much higher interconnectedness in the EMU sovereign bond yields for observations recorded during the period of 2010– 2012 marked by the European debt crisis. We also find some evidence to purport that the European Central Bank (ECB) sovereign bond purchases as interventions in debt markets under the securities markets programme (SMP) from May 2010 to September 2012 did have a positive impact on EMU yields falls. In addition, the two new purchase programmes, namely the ABS purchase programme (ABSPP) and the third covered bond purchase programme (CBPP3) announced by the ECB in September 2014 to enhance transmission of monetary policy could explain the decline in yields at the end of 2014. Our findings also suggest that the European ban on purchases of naked sovereign CDS did have negative consequences as claimed by the 4 International Monetary Fund.

The structure of the remainder of this paper is as follows. Section 2.1 presents a description of the considered datasets used in studying the European debt crisis. Section 2.2 presents an overview of recurrence networks, recurrence quantification analysis and complex network measures useful in studying nonlinear dynamics of underlying time series data. Section 2.3 provides information on available programming packages for the implementation of the method. The empirical application of the method to studying the European sovereign debt crisis is then provided. Finally, in Section 3, we discuss the results and provide concluding remarks on the advantages of this approach in the area of economics and finance. In particular, we provide conclusions and policy implications based on our findings to enhance financial stability in the European Monetary Union.

2. Data & Method

2.1. Data description The data used in our empirical analysis consist of daily 10-year government bond yields for eleven European Monetary Union (EMU-11) countries.

The EMU-11 economies used in this study is composed of the periphery group of countries: Portugal, Ireland, Italy, Greece, Spain; and the core group of countries: Austria, Germany, The Netherlands, Belgium, France, and Finland. These peripheral countries have attracted significant amount of attention from the markets and the media due to high debt levels and low levels of growth. Our choice of using the EMU-11, which includes countries with different characteristics is to enhance a more diversified and rich analysis 5 of the European debt crisis. Sovereign bond yields shows how much interest a government needs to pay in order to borrow money from investors. Higher interest rate demanded by investors due to fear of failure that the governments may not be able to pay them back usually lead to what is referred to as sovereign debt crisis. The idea is to empirical investigate the EMU-11 sovereign debt crisis by examining the network dynamics of the government bond yields over the period (01/01/2007–31/12/2014). The start date of the sample is chosen in order to study dynamics prior and during the Sovereign debt crisis. The empirical analysis also focuses on the network dynamics of Sovereign credit default swaps (SCDS) prices for the EMU-11 economies during the European debt crisis. In this respect, we use daily data on 5-year sovereign CDS prices over the same period as the bond yields. Our daily data are sourced from Bloomberg.

2.2. Recurrence quantification & network analysis

The recurrence network analysis is a nonlinear approach based on the mix of recurrence analysis (Marwan et al. (2007); Thiel et al. (2006)) and complex network revealing temporal pattern of mutual recurrence of states and extracting essential information about the main dynamics of an underlying time series data (Marwan et al. (2009); Donner et al. (2010, 2011); Donges et al. (2012)). For any given time series, denote by Xt, we can generate an embedded version in phase space via Takens’ embedding theorem (Takens (1981)). This is achieved by first estimating the embedding dimension and time delay (see Takens (1981); Marwan et al. (2007); Kantz and Schreiber (1997); Addo et al. (2014) and the references therein). In this work, we make use of an unembedded multivariate time series such that each time index (i) 6 corresponds to a state vector Xi with components being the observation of each subprocess at that time index. Unembedding the time series has its advantages when performing recurrence quantification analysis (RQA)(Thiel et al. (2006); Zbilut and Webber (1992); Marwan and Kurths (2002); Trulla et al. (1996)). The adjacency matrix of an unweighted and undirected complex network associated to the underlying time series is given by

–  –  –

where δi,j denote Kronecker’s delta, ε is the recurrence threshold, subscripts i, j ∈ {1, 2, · · ·, T } are time indexes and Ri,j (·) is the recurrence matrix associated with the underlying time series Xt. The recurrence matrix (Marwan et al. (2007)) of Xt is defined by

–  –  –

where · denotes a suitable distance norm (i.e. say the supremum norm), and Θ(·) is the Heaviside function. The threshold ε for the recurrence analysis √ is chosen to be equal to σ m/10, where σ is the fluctuation level in signal, m is the embedding dimension of the signal (Letellier (2006)). Note that m = 1 implies that the time series data is unembedded. Alternatively, one can choose the threshold in such a way, that its value corresponds to 10% of the maximum phase space diameter or such that the recurrence rate is 10% (Schinkel et al. (2008); Thiel et al. (2002); Marwan et al. (2007)). The plot of the recurrence matrix is referred to as the recurrence plot. This concept of recurrence plot has recently gained considerable attention in economics and finance (see Fabretti and Ausloos (2005); Zbilut (2005); Crowley and Schultz (2011); Addo et al. (2013, 2014), and the references therein). In this 7 study, we will make use of measures for the quantification of recurrence plots.

These measures are usually referred to as recurrence quantification analysis (RQA) developed by Zbilut and Webber (1992); Marwan and Kurths (2002);

Trulla et al. (1996) and also detailed in Marwan et al. (2007). The measures include the recurrence rate (in %), determinism (in %), laminarity (in %) and the averaged diagonal line length. See Appendix A for details. These measures will be used in studying the time dependence and the detection of transitions in the dynamics of our underlying time series data. It is worth pointing out that RQA is build upon temporal structures in the form of diagonal and vertical lines, thus placing under the class of correlative-based methods of time series analysis (Zbilut and Webber (1992); Marwan and Kurths (2002)).



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